Question

If sintheata+ costheata=a and sectheata+ cosectheata=b,then the value of b(a square-1) is equal to

Answer 1

Answer:

2a

Step-by-step explanation

secA + cosecA=b

(1/sinA) +(1/ cosA)=  b

(sinA+ cosA)/sinA.cosA =b

a/sinA.cosA=b                                                   (sinA+cosA=a)

sinA.cosA=a/b         -----(1)

now,

sinA+ cosA = a

squaring  on both  sides

(sinA)^2 +(cosA)^2+2.sinA.cosA =a^2

1 +2.(a/b)=a^2                        ((sinA)^2+(cosA)^2=1 & from (1))

2(a/b)=a^2 -1

2a= b(a^2 -1)